Subgroups — #3674⋊C₃ #88515

Order 432.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	3₋¹⁺²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#216	—	3	1	no	maximal
5	#3674	C₃	1	1	yes	maximal, characteristic, complemented
6	C₄×3₋¹⁺²	—	2	1	no	—
7	C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
8	3₋¹⁺²⋊C₄	—	2	1	no	—
9	C₃²×Q₈	D₃	1	1	yes	characteristic
10	C₃×Dic₆	—	3	1	no	—
11	C₃×C₃⋊C₈	—	3	1	no	—
12	Q₈×C₉	—	2	1	no	—
13	Q₈×C₉	C₂×C₃	1	1	yes	characteristic
14	Dic₁₈	C₂×C₃	1	1	yes	characteristic
15	C₉⋊C₈	C₂×C₃	1	1	yes	characteristic
16	C₂×3₋¹⁺²	D₄	1	1	yes	characteristic
17	C₃×Q₁₆	—	9	1	no	—
18	#216	—	3	1	no	—
19	C₃²×C₄	—	2	1	no	—
20	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
21	C₃×Dic₃	—	6	1	no	—
22	C₄×C₉	—	2	2	no	—
23	C₄×C₉	—	2	1	no	—
24	C₄×C₉	—	2	1	no	—
25	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
26	Dic₉	—	2	1	no	—
27	3₋¹⁺²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₃×Q₈	—	6	1	no	—
29	C₃×Q₈	—	9	1	no	—
30	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
31	Dic₆	—	3	1	no	—
32	C₃×C₈	—	9	1	no	—
33	C₃⋊C₈	—	3	1	no	—
34	C₂×C₃²	#67	1	1	yes	characteristic
35	C₂×C₉	—	2	1	no	—
36	C₂×C₉	C₃×D₄	1	1	yes	characteristic
37	Q₁₆	—	9	1	no	Sylow
38	C₃×C₄	—	2	1	no	—
39	C₃×C₄	—	6	1	no	—
40	C₃×C₄	—	6	1	no	—
41	C₃×C₄	—	18	1	no	—
42	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
43	Dic₃	—	6	1	no	—
44	C₃²	#216	1	1	yes	characteristic
45	C₉	—	2	1	no	—
46	C₉	C₃×Q₁₆	1	1	yes	characteristic, complemented
47	Q₈	—	9	1	no	—
48	Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic
49	C₈	—	9	1	no	—
50	C₂×C₃	—	6	1	no	—
51	C₂×C₃	C₃×#67	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	18	1	no	—
54	C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
55	C₃	—	6	1	no	—
56	C₃	C₃×#216	1	1	yes	characteristic
57	C₂	#611⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#611⋊C₃
commutator, cosocle	C₄×C₉	C₂²×C₃
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	Q₈×3₋¹⁺²	C₂
socle	C₂×C₃	C₃×#67
prime radical	C₂×C₃²	#67
hypercenter	Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. #3674	C₃	semidirect
27. 3₋¹⁺²	Q₁₆	semidirect
46. C₉	C₃×Q₁₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₈×3₋¹⁺²	2
3₋¹⁺²⋊Q₈	2
3₋¹⁺²⋊C₈	2
C₃×#216	3
#3674	3

Subgroups — #3674⋊C3 #88515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3674⋊C₃ #88515